Various techniques, including computed tomography (CT), positron emission tomography (SET), and ultrasonic reflective tomography (URT), can be used to generate an image from a scanned data set of a subject. For example, a CT scanning system is used to produce cross-sectional images of a portion or "slice" of a patient. A CT scanning system 10, shown in FIG. 1, includes a source of collimated X-rays 11 and an array of X-ray detectors 12. A patient P is positioned between the source 11 and detectors 12. The X-ray source 11 revolves about the patient so that X-ray attenuation measurements may be obtained from many different angles. The X-ray source 11 may produce a fan-shaped beam 13 (or parallel beams by means of a translational movement of the x-ray source) that passes through the patient and impinges upon the detectors 12, generating attenuation measurements. A complete scan of the patient includes a set of X-ray attenuation measurements which are made at different angular orientations of the X-ray source 11 and detectors 12 in one revolution about the patient.
An attenuation measurement at a given orientation is referred to as a view, and the set of measurements at a view form a transmission profile. Each transmission profile contains an array of digital data samples. Each digital data sample represents the amount of the attenuated X-ray collected by one of the detectors. The profiles form a complete scan and are stored in memory as raw, unprocessed data. In two-dimensional CT raw data, the angular coordinate is referred to as the azimuth direction, and the other coordinate is referred to as the radial direction. The transmission profiles from a scan are processed to reconstruct an image which reveals the anatomical structures in a cross-section or slice of the patient. The reconstruction process converts the attenuation measurements from a scan into integers called CT numbers or Hounsfield units.
Convolution backprojection (CBP) is one technique for image reconstruction. CBP includes two general processing steps: (1) a finite impulse response, also referred to as kernel, is convoluted with each transmission profile; and (2) a line integral following the trace of a curve is performed to generate each output image pixel. This curve contains all the points with the maximum attenuation on each transmission profile caused by the target of the output pixel. For a fan beam system, an array of weights is multiplied with the data samples during the line integral process. When higher accuracy is required, the output of the first step is oversampled for a finer sample spacing such that the backprojection step may follow a more precise curve. CBP has a relatively slow processing throughput rate as compared to the direct Fourier method described in the following paragraph.
Another image reconstruction technique uses the direct Fourier method. The direct Fourier method has three basic processing steps: (1) performing a fast Fourier transform (FFT) for each transmission profile, resulting in a two-dimensional Fourier spectrum of the image in polar coordinates, with uniform spacing in the azimuth angle and radial frequency; (2) resampling and local averaging to convert the spectrum from polar coordinates into Cartesian coordinates, with uniform spacing in each of the two perpendicular axes; and (3) performing a two-dimensional inverse FFT to transform the spectrum back into the space domain, resulting in a cross-sectional image of the patient. The direct Fourier method provides improved computation efficiency over CBP. However, the image quality of the direct Fourier method is relatively poor due to the spectral phase error induced from the resampling process. Also, generally the direct Fourier method compatible with a parallel beam CT scanning system, and not with a fan beam CT scanning system.
The inventor of the present invention recognized the limitations of the prior art image reconstruction techniques discussed above and developed an improved technique for increasing the throughput rate of the backprojection process while maintaining image quality. The inventor, recognized that image reconstruction could be performed by fast two-dimensional Fourier circular convolution (FFCC). This backprojection process involves Fourier transform in both the radial dimension and the azimuthal dimension. By incorporating FFCC into the image reconstruction process, the number of computations may be reduced by up to 68%, while the quality of the reconstructed image is commensurate with the known CBP technique.
Further, the FFCC technique yields efficient memory access patterns when implemented on workstations or similar computer systems. The cost of the computer hardware, including memory, is typically a significant part of the cost of a CT scanning system. Based on the current trend of the rapidly decreasing cost of workstations and similar computer systems, the present invention may be implemented on a relatively cost-effective computer system. Therefore, the present invention helps reduce the cost of medical services, benefiting both the patient and provider.
Also, the inventor developed a reconstruction technique that may be implemented with both fan beam and parallel beam CT systems. Further, the image reconstruction technique of the present invention may be implemented in PET, URT, and other applications where the convolution backprojection technique may be used.
The present image reconstruction technique may be implemented in a variety of computing systems, including client/server systems. The technique may be implemented in hardware or software, or a combination of both. Preferably, the technique is implemented in computer programs executing on programmable computers that each include a processor, a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device. Program code is applied to data entered using the input device to perform the functions described above and to generate output information. The output information is applied to one or more output devices.
Each program is preferably implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the programs can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language.
Each such computer program is preferably stored on a storage medium or device (e.g., ROM or magnetic diskette) that is readable by a general or special purpose programmable computer for configuring and operating the computer when the storage medium or device is read by the computer to perform the procedures described in this document. The system may also be considered to be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner.
Other features and advantages will become apparent from the following description, including the drawings, and from the claims.
It is, therefore, an object of the present invention to provide a system and method for reconstructing images of a cross-sectional area from raw, scanned data.
It is another object of the invention to reconstruct images by using fast two-dimensional Fourier circular convolution.